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Invariant tori for a class of affine Anosov mappings with a quasi-periodic forcing

Part of: Smooth dynamical systems: general theory Dynamical systems with hyperbolic behavior

Published online by Cambridge University Press:  11 September 2025

XINYU BAI ,
ZENG LIAN ,
XIAO MA Open the ORCID record for XIAO MA [Opens in a new window]  and
HANG ZHAO
XINYU BAI
Affiliation:
School of Mathematics, https://ror.org/011ashp19 Sichuan University , Chengdu, Sichuan 610016, China (e-mail: 23210180080@m.fudan.edu.cn, lianzeng@scu.edu.cn, hangzhaoscu@163.com)
ZENG LIAN
Affiliation:
School of Mathematics, https://ror.org/011ashp19 Sichuan University , Chengdu, Sichuan 610016, China (e-mail: 23210180080@m.fudan.edu.cn, lianzeng@scu.edu.cn, hangzhaoscu@163.com)
XIAO MA*
Affiliation:
School of Mathematical Sciences, https://ror.org/04c4dkn09 University of Science and Technology of China , Hefei, Anhui, China
HANG ZHAO
Affiliation:
School of Mathematics, https://ror.org/011ashp19 Sichuan University , Chengdu, Sichuan 610016, China (e-mail: 23210180080@m.fudan.edu.cn, lianzeng@scu.edu.cn, hangzhaoscu@163.com)
*
e-mail: xiaoma@ustc.edu.cn
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Abstract

In this paper, we consider a class of affine Anosov mappings with a quasi-periodic forcing and show that there is a unique positive integer m, which only depends on the system, such that the exponential growth rate of the number of invariant tori of degree m is equal to the topological entropy.

Keywords

affine Anosov mappingsquasi-periodic forcinginvariant torustopological entropy

MSC classification

Primary: 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
Secondary: 37C35: Orbit growth

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , First View , pp. 1 - 16
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

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